Finite Group Databasebeta

← #15773499

Subgroups — #15773499

Order 3328.

446 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119741C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic, complemented
3#13112843C212yesmaximal, complemented
4#13112840C212yesmaximal
5C13×#1467C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88200—21no—
8C2×C4×D52C411yescharacteristic
9C13×#432—21no—
10C2×#88076—21no—
11#11718652C411yescharacteristic
12#11718652C2211yescharacteristic
13#11718648—21no—
14#11718644C411yescharacteristic
15#11718644C2211yescharacteristic
16#11718601—21no—
17#11718601—21no—
18#11718597C411yescharacteristic
19C4×#6099—21no—
20C13×#324—21no—
21C13×#324C2212yes—
22#11718122C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×C4×D13—21no—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34#88200—44no—
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6099—22no—
45C4×D52—41no—
46C4×D52—41no—
47C13×C4⋊C8—41no—
48C13×C22⋊C8—22no—
49C13×#97—41no—
50#88076—24no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56#88043—41no—
57C4×#1055—41no—
58#11778—131nomaximal, Sylow
59C23×D13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C2×D52—41no—
74C2×D52—42no—
75C2×C4×D13—42no—
76C2×C4×D13—42no—
77C2×C4×D13—42no—
78C2×C8×C13—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88#6103—42no—
89#6103—42no—
90#6103—42no—
91#6103—41no—
92#6103—41no—
93#6103—42no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96#6101—42no—
97#6101—42no—
98#6099—24no—
99#6099—42no—
100C2×#1055—42no—
101#2536—131no—
102C4×#101—131no—
103#1467D1311yescharacteristic, complemented
104#1346—132no—
105#1345—132no—
106C23×C13C2×C22⋊C411yescharacteristic
107C22×D13—22no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111C22×D13—41no—
112C22×D13—41no—
113C22×D13—41no—
114Q8×C13—44no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#10412yes—
132C2×C4×C13AGL(1,ℤ/8)12yes—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142D52—42no—
143D52—42no—
144C4×D13—84no—
145C8×C13—82no—
146#1055—44no—
147C2×C22⋊Q8—261no—
148C2×C4×Q8C2×D1311yescharacteristic
149C2×C4×D4—131no—
150#432—21no—
151C2×#101—261no—
152C4×M16—261no—
153#398—131no—
154#398—131no—
155#394—131no—
156#394—131no—
157#388—261no—
158#388—261no—
159#382—131no—
160#380—261no—
161#343—132no—
162#324—21no—
163#324C2×D1312yes—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13C2×#9911yescharacteristic
167C22×C13#41811yescharacteristic
168C22×C13C2×#10411yescharacteristic
169C2×D13—42no—
170C2×D13—42no—
171C2×D13—42no—
172C2×D13—81no—
173C2×D13—81no—
174C2×D13—81no—
175C2×D13—81no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184Dic13—81no—
185Dic13—81no—
186Dic13—81no—
187C22×Q8D5211yescharacteristic
188C22×D4—131no—
189C23×C4—261no—
190C2×M16—262no—
191C22⋊Q8—524no—
192C4×Q8—41no—
193C4×Q8—41no—
194C4×D4—521no—
195C4×D4—521no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4C4×D1311yescharacteristic
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22×D1311yescharacteristic
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C42C4×D1311yescharacteristic
209C2×C42D5211yescharacteristic
210C2×C42C22⋊D1311yescharacteristic
211C4⋊C8—41no—
212#101—264no—
213C22⋊C8—22no—
214#97—41no—
215#97—521no—
216C4×C8—521no—
217#95—131no—
218#95—131no—
219#95—261no—
220#95—261no—
221#95—261no—
222C2×C13—21no—
223C2×C13—21no—
224C2×C13#150711yescharacteristic
225C2×C13#212011yescharacteristic
226C2×C13#213311yescharacteristic
227D13—82no—
228C24—261no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×D4—521no—
233C2×D4—522no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—522no—
238C22×C4—522no—
239C22×C4—522no—
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4C2×D5211yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—264no—
248M16—522no—
249C2×C8—42no—
250C2×C8—522no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—521no—
255C4⋊C4—522no—
256C4⋊C4—522no—
257C4⋊C4—522no—
258C22⋊C4—522no—
259C22⋊C4—522no—
260C22⋊C4—522no—
261C22⋊C4—522no—
262C22⋊C4—521no—
263C22⋊C4—521no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C13#1177811yescharacteristic, complemented, Sylow
271C23—262no—
272C23—521no—
273C23—521no—
274C23—521no—
275C23—521no—
276C23—521no—
277C23—521no—
278C23C2×#610311yescharacteristic
279Q8—44no—
280D4—522no—
281D4—522no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—1044no—
306C2×C4#8804611yescharacteristic
307C2×C4#8804611yescharacteristic
308C2×C4#8806512yes—
309C2×C4#8816212yes—
310C8—82no—
311C8—524no—
312C22—21no—
313C22—21no—
314C22—522no—
315C22—522no—
316C22—522no—
317C22—1041no—
318C22—1041no—
319C22—1041no—
320C22—1041no—
321C22C2×#8804611yescharacteristic
322C22#1171879211yescharacteristic
323C22C2×#8806511yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—1041no—
333C4—1041no—
334C4—1041no—
335C2—21no—
336C2—21no—
337C2—1042no—
338C2#1311335311yescharacteristic
339C2#1311647511yescharacteristic
340C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11778
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C4×#88076C2semidirect
3. #13112843C2semidirect
5. C13×#1467C2semidirect
103. #1467D13semidirect
270. C13#11778semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131197412
C4×#880762
#131128432
#131128402
C13×#14672
#1177813